(Blender Internal) How to apply chroma key to videos on a plane?
This is a simple node setup in Blender's Compositor.  If you're unfamiliar with this part of Blender, leave a comment and I'll add step by step as to how to get into it.



If only wishing to remove the green and not overlay a background, i.e. have a video with just the effects, delete the BKD movie Node. Replace the Alpha Over Node with a "Set Alpha" node.  Connect it as shown below.



You'll end up with an alpha layered output.  If not needing the alpha layer, render in H264 AVI (RGB).  (or your favorite format) 

If you do want the Alpha layer, you'll need to render the video as a series of Alpha layered .png images.  Make sure to create/select a special folder for these.  There'll be a lot!
These can be compressed into a single file for storage.

I've found it easier if the key colour isn't as bright as it's shown in the top pic.  (bottom of the keying node)

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Getting the resultant movies onto a plane - 

Simply texture the plane using "Generated" mapping for starters to see how it goes.  You can revert to UV mapping if you prefer.

In the image properties "Image" tab, make sure to click on "Auto Refresh" so the movie or image sequence will play.